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We study linear polarization from scattering of light on a cloud of relativistic electrons. We assume that the cloud is hovering above an accretion disc, or it is in an accelerated motion under the combined influence of the radiation and gravitational fields near an accreting black hole. At first we derive simple and general analytical formulae for the Stokes parameters. These formulae are then used in calculations of the temporal evolution of the observed signal. We find that higher-orderdoi:10.1017/s1743921307005558 fatcat:n36loxirvjebzcnm7vrlkl5qeq